Modelling the TGFs and the electron positron beams of a negative stepped lightning leader

We model which spectrum of gamma-ray flashes, electron beams and electron-positron beams are created by negative leaders while they step upward in a thundercloud; we resolve the distributions of photons, electrons and positrons both in energy and in space. To do this, we implement a simple model of a stepped leader and calculate how electrons are accelerated in the highly enhanced electric field ahead of the leader tip, and how photons and electron positron pairs appear and propagate. Our calculations are based on the Monte Carlo code of C. Li et al. that was used in 2009 within a spatially hybrid code to calculate electron run-away from streamers. We have extended this code with relativistic equations of motion and with cross sections for ionization and elastic scattering at relativistic energies and Bremsstrahlung of electrons; furthermore we use cross sections for inelastic processes at non-relativistic energies. For the photons we include Compton scattering, pair production and photo ionization. Bremsstrahlung and pair production are modelled according to our recent analysis of appropriate cross sections for small atomic numbers and for electron energies above 1 keV [preprint available on http://arxiv.org/abs/1202.4879]. We also study how the geomagnetic field influences the results at different latitudes.